Compared with traditional RNN and other excellent variants of RNN [1]}, FG-LSTM can choose to update the learned parameters at the time point \(t\)  of irregular sampling. This allows the FG-LSTM to work with asynchronously sampled irregular time-series data.
We can then rewrite the regular LSTM cell update equations for \(c_t\)  and \(h_t\) , using proposed cell updates \(c_t^{\widetilde{}}\)  and \(h_t^{\widetilde{}}\)  mediated by the feature gate \(s_t\)  :
\(& i_{t}=\sigma _{i}(x_{t}W_{xi}+h_{t-1}W_{hi}+w_{ci}\odot c_{t-1}+b_{i}) \\& f_{t}=\sigma _{f}(x_{t}W_{xf}+h_{t-1}W_{hf}+w_{cf}\odot c_{t-1}+b_{f}) \\ & c_t^{\widetilde{}}=f_t\odot c_{t-1}+i_t\odot \tanh _c(x_tW_{xc}+h_{t-1}W_{hc}+b_c)\\& c_t=s_t\odot c_t^{\widetilde{}}+(1-s_t)\odot c_{t-1}\\& o_{t}=\sigma _{o}(x_{t}W_{xo}+h_{t-1}W_{ho}+w_{co}\odot c_{t}+b_{o}) \\& h_t^{\widetilde{}}=o_t\odot \tanh _h(c_t^{\widetilde{}})\\& h_t=s_t\odot h_t^{\widetilde{}}+(1-s_t)\odot h_{t-1} \) 
